Practise the method.
Example 1
An open hollow square prism has uniform wall thickness 2cm, height 6cm and material volume 384cm3. The hole passes right through. Find the total exposed surface area, including inner walls, outer walls and both end rims, in cm2.
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Answer: 512
- If the outer side is x, the inner side is x−4.
- Material volume gives 6[x2−(x−4)2]=384
- x=10 and the inner side is 6.
- Wall areas total 4(10+6)×6=384.
- The two rims total 2(100−36)=128.
- Total =512cm2.
Example 2
Two rectangular prisms are joined. The base is 10cm×5cm×4cm. The upper prism has base 2cm×3cm and height H. Their total volume is 224cm3. Find the total exposed surface area, including the bottom but excluding the joined faces, in cm2.
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Answer: 260
- Upper volume =224−200=24
- H=2×324=4.
- Add both prism surface areas
- remove the two joined 2×3 faces: 2(50+40+20)+2(6+8+12)−12=260cm2.
Example 3
An open hollow square prism has uniform wall thickness 1cm, height 12cm and material volume 384cm3. The hole passes right through. Find the total exposed surface area, including inner walls, outer walls and both end rims, in cm2.
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Answer: 832
- If the outer side is x, the inner side is x−2.
- Material volume gives 12[x2−(x−2)2]=384
- x=9 and the inner side is 7.
- Wall areas total 4(9+7)×12=768.
- The two rims total 2(81−49)=64.
- Total =832cm2.